how many "modern" mathematicians support Pythagoras;s and Plato's take on numbers being the perfect noumenal

Question

or occultaded forms behind manifested reality?

Answer 1

I have no idea of how to even discern "how many contemporary mathematicians" think of numbers as abstract constructs of the mind, as opposed to something we've learned from practical reality. I can't think of a single theorem or even axiom in mathematics that depends on making such a distinction, so any held opinions about that would be mostly private, and most do not publish their private sentiments on such matters. Philosophers, on the other hand, must keep busy, and they write copiously about whether or not numbers are perfect noumenals. My philosophical question is, "How may this be important to the way mathematics is done or works?" Would it change a single integral, or group, or calculus of forms, or invalidate any geometry, Euclidean or non-Euclidean?

Most modern mathematicians will probably agree that it's the structure that matters, that edifice of conclusions or theorems that can be drawn from a set of definitions or axioms. Frequently, such structure takes a life of its own, independent from the objects it's supposedly based on. It's as if after a structure has gone up, the scaffolding may be taken down. So, while it may be of philosophical interest as to whether or not numbers are just abstract constructs of the mind, it may be that most mathematicians today don't care, because it's not yet shown how it could affect any structure in mathematics.

Answer 2

Short answer----NONE!

Pythagoras had his cult. Mathematics is anything BUT magic and superstition.